The story
Na pososhok (на посошок) is what Russians say over the last drink before a guest leaves. Na means 'for' or 'to', and pososhok is a diminutive of posokh, a staff: the long stick of a pilgrim, a shepherd or a traveller, and also a bishop's crozier. So the toast is, quite literally, to the little staff, the one you will lean on for the journey home.
The word kept both lives for a while. In Alexander Radishchev's Journey from St Petersburg to Moscow, written at the end of the 18th century, a pososhok is still an actual walking stick that the narrator picks up before setting off on foot. By 1858, in Aleksey Pisemsky's novel A Thousand Souls, a character asks to take a pososhok for the road and pours himself a glass of vodka. The stick had become the drink.
English has one for the road, which does the same job without the image. Older English had the stirrup cup, the parting drink taken after mounting a horse; Walter Scott, in The Bride of Lammermoor, sets it beside the Gaelic doch-an-dorroch. All three name the same moment: the goodbye has started, but nobody has quite left.
A flat on the edge of Moscow, close to midnight. Coats are on, someone is hunting for a missing glove, and the host appears in the hallway with the bottle and four small glasses. Nobody argues. Na pososhok.